Green's Function Solution of Multiple Shallow-Buried Cavities and Inclusions in Elastic Semi-Space

Abstract

In engineering composite materials, earthquake engineering and modern municipal construction, it can be found that there are shallow-buried cavity or inclusion structure near surface. When structure is impacted by dynamic load, scattering field will be produced because of the cavity or the inclusion, and it could cause dynamic stress concentration at the edge of the cavity or inclusion. In this paper, Green's Function is studied, which is the solution of displacement field for elastic semi-space with multiple shallow-buried cavities and inclusions while bearing anti-plane harmonic line source force at any point. In the complex plane, considering the symmetry of SH-wave scattering, the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field impacted by multiple cylindrical cavities and inclusions are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the stress or displacement condition of the cylindrical cavities and inclusions in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. By solving these algebraic equations the value of the unknown coefficients can be obtained. So the total wave displacement field could be got. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical cavities, inclusions and the location of the line source force.